Terms Of Moments Research Articles

Berry-Esseen bounds for the multivariate ℬ-free CLT and operator-valued matrices

We provide bounds of Berry-Esseen type for fundamental limit theorems in operator-valued free probability theory such as the operator-valued free Central Limit Theorem and the asymptotic behaviour of distributions of operator-valued matrices. Our estimates are on the level of operator-valued Cauchy transforms and the Lévy distance. We address the single-variable as well as the multivariate setting for which we consider linear matrix pencils and noncommutative polynomials as test functions. The estimates are in terms of operator-valued moments and yield the first quantitative bounds on the Lévy distance for the operator-valued free Central Limit Theorem. Our results also yield quantitative estimates on joint noncommutative distributions of operator-valued matrices having a general covariance profile. In the scalar-valued multivariate case, these estimates could be passed to explicit bounds on the order of convergence under the Kolmogorov distance.

Time-Domain Hybrid Method for the Coupling Analysis of Power Line Network With Curved and Multidirectional Segments

Currently, numerical methods used for the coupling analysis of power line network, integrating the structural features of curve and multiorientations, are still rare. An efficient time-domain hybrid method consisting of the finite-difference time-domain (FDTD) method, transmission line (TL) equations of Agrawal model, coordinate transform, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameter cascade techniques is presented in this work, which can realize the fast-coupling simulation of power line network with curved and multidirectional segments (PLN-CMS). First, the overall structure of PLN-CMS is decomposed into a cascade network of multiple independent curved power line segments and connecting nodes, and the ports of each power line segments are equivalent modeled by matched loads. Then, the coupling model of each curved power line segments with arbitrary orientation is constructed via the TL equations of Agrawal model combining with the coordinate transform technique, and the transient responses on these curved power line segments and matched loads are solved by the FDTD method. Finally, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameter cascade technique is applied to deal with the scattering voltages at the connecting nodes to realize the data transmission of interference signals between these curved power line segments. Numerical simulations for the coupling analysis of PLN-CMS constructed by single line or double lines on the ground excited by strong electromagnetic pulse are considered to verify the correctness and efficiency of the proposed method by comparing with the method of moments in terms of precision and time consumption. On this basis, the coupling characteristics of lightning electromagnetic pulse acting on the actual three-phase power line network are simulated and analyzed.

On the number variance of zeta zeros and a conjecture of Berry

AbstractAssuming the Riemann hypothesis, we prove estimates for the variance of the real and imaginary part of the logarithm of the Riemann zeta function in short intervals. We give three different formulations of these results. Assuming a conjecture of Chan for how often gaps between zeros can be close to a fixed non‐zero value, we prove a conjecture of Berry (1988) for the number variance of zeta zeros in the non‐universal regime. In this range, Gaussian unitary ensemble statistics do not describe the distribution of the zeros. We also calculate lower order terms in the second moment of the logarithm of the modulus of the Riemann zeta function on the critical line. Assuming Montgomery's pair correlation conjecture, this establishes a special case of a conjecture of Keating and Snaith (2000).

High-Degree Collisional Moments of Inelastic Maxwell Mixtures—Application to the Homogeneous Cooling and Uniform Shear Flow States

The Boltzmann equation for d-dimensional inelastic Maxwell models is considered to determine the collisional moments of the second, third and fourth degree in a granular binary mixture. These collisional moments are exactly evaluated in terms of the velocity moments of the distribution function of each species when diffusion is absent (mass flux of each species vanishes). The corresponding associated eigenvalues as well as cross coefficients are obtained as functions of the coefficients of normal restitution and the parameters of the mixture (masses, diameters and composition). The results are applied to the analysis of the time evolution of the moments (scaled with a thermal speed) in two different nonequilibrium situations: the homogeneous cooling state (HCS) and the uniform (or simple) shear flow (USF) state. In the case of the HCS, in contrast to what happens for simple granular gases, it is demonstrated that the third and fourth degree moments could diverge in time for given values of the parameters of the system. An exhaustive study on the influence of the parameter space of the mixture on the time behavior of these moments is carried out. Then, the time evolution of the second- and third-degree velocity moments in the USF is studied in the tracer limit (namely, when the concentration of one of the species is negligible). As expected, while the second-degree moments are always convergent, the third-degree moments of the tracer species can be also divergent in the long time limit.

Propaganda istorica si culturala reflectata in colectii grafice muzeale

The Erdélyi Museum in Cluj, the forerunner of the National Museum of History of Transylvania in Cluj‑Napoca, was established in 1859, at a peak moment in terms of interest in national history. Graphic portraits are an important sample of collections and motivation is given by the desire to draw educational directions in the knowledge of the general public. Researching the old museum collections we note that an essential element in the Transylvanian educational program was the promotion of the cult of the great historical and cultural personalities of Europe. This trend is particularly visible in the graphic arts where in the 19th century lithography was required, which offered the possibility of multiplying the prints at affordable costs. Characters belonging to Transylvanian space, culture and history were preferred, but the graphic collections also enjoy important European personalities.

Исследование различных подходов к управлению двухмассовыми объектами

The reasons for elastic oscillations occurring in the mechanisms of multi-mass objects are considered. Various control systems for complex two-mass objects are analyzed. A mathematical description of a twomass system interconnected through an elastic drive belt is provided. According to the given system of equations, a block diagram of the object under consideration has been constructed in the mathematical environment of MatLab and Simulink. The synthesis and comparative analysis is conducted for the following control systems for a two-mass object: slave control with external feedback on the speed of the first mass; multiloop slave regulation; modal control; subordinate regulation using a correction factor and a neurocontroller with a reference model. The resulting graphs of transient processes in terms of moment and speed of the driven pulley of the considered twomass system with an elastic replacement belt are presented and analyzed. The simulation results have shown that control systems with a modal controller and a neurocontroller show good results in the problem of damping elastic vibrations of a two-mass system in comparison with other considered control systems.

Dynamic Behavior of Helical Piles in Dry and Liquefiable Soils using Scaled Shake Table Tests

The dynamic behavior of helical piles with different numbers of helices as well as a single slender shaft was examined through a series of scaled shake table tests. Multiple shakings were applied during each test series to evaluate the seismic behavior of the helical piles and the slender shaft considering different response parameters. A considerable ground settlement was observed during the first shaking in each test series, whereas negligible helical pile and slender shaft settlements were measured during all tests. The dynamic response of the helical piles was evaluated based on their bending moment variation along the depth and various measured response parameters at the model superstructure level. The bending moment variation indicated a similar trend along the depth for the helical piles and the slender shaft: the maximum moment was consistently observed at the boundary between dense and liquefiable layers. The observed bending moments along the depth increased with increases in input motion amplitude and superstructure weight. Densification of the liquefiable layer during different test series reduced the maximum bending moment along the depth for each pile due to increased relative density. Increasing the number of helices enhanced the dynamic performance of the helical piles compared to the slender shaft in terms of maximum bending moment, maximum horizontal displacement, residual horizontal displacement, and superstructure acceleration in different ground conditions.

Recent advances in the chemistry and applications of fluorinated metal-organic frameworks (F-MOFs).

Metal-organic frameworks are a class of porous crystalline materials based on the ordered connection of metal centers or metal clusters by organic linkers with comprehensive functionalities. The interest in these materials is rapidly moving towards their application in industry and real life. In this context, cheap and sustainable synthetic strategies of MOFs with tailored structures and functions are nowadays a topic widely studied from different points of view. In this review, fluorinated MOFs (F-MOFs) and their applications are investigated. The principal aim is to provide an overview of the structural features and the main application of MOFs containing fluorine atoms both as anionic units or as coordinating elements of more complex inorganic units and, therefore, directly linked to the structural metals or as part of fluorinated linkers used in the synthesis of MOFs. Herein we present a review of F-MOFs reported in the recent literature compared to benchmark compounds published over the last 10 years. The compounds are discussed in terms of their structure and properties according to the aforementioned classification, with an insight into the different chemical nature of the bonds. The application fields of F-MOFs, especially in sustainability related issues, such as harmful gas sorption and separation, will also be discussed. F-MOFs are compounds containing fluorine atoms in their framework and they can be based on: (a) fluorinated metallic or semi-metallic anionic clusters or: (b) fluorinated organic linkers or (c) eventually containing both the building blocks. The nature of a covalent C-F bond in terms of length, charge separation and dipole moment sensibly differs from that of a partly ionic M-F (M = metal) one so that the two classes of materials (points a and b) have different properties and they find various application fields. The study shows how the insertion of polar M-F and C-F bonds in the MOF structure may confer several advantages in terms of interaction with gaseous molecules and the compounds can find application in gas sorption and separation. In addition, hydrophobicity tends to increase compared to non-fluorinated analogues, resulting in an overall improvement in moisture stability.

Numerical investigation of the dynamic soil-structure interaction of concrete buildings

This research is carried out to investigate and assess the dynamic soil-structure interaction features related to a reinforced concrete building. Numerical analysis and mathematical simulations were performed depending on the ABAQUS® software package to achieve the study goal. Structures with floor numbers ranging between one and ten were modelled and simulated, and soil characteristics were explored and measured in terms of base shear, axial force, moment, and displacement, taking into account dynamic soil-structure interaction principles. In addition, the effect of soil type on the building stability and soil performance was assessed and examined. The research findings revealed that the base shear for a five-floor building frame decreases by 5% from soft to medium soil and by 23% from medium to hard soil. Also, the base shear for a five-floor building frame reduces by 5% from soft to medium soil and by 23% from medium to hard soil. The base shear for a shear wall system with ten stories on medium soil is 20% less than that on soft soil. On hard soil, this outcome is lowered by 12%. The axial force for a five-floor building frame decreases by 2% from mild to medium soil and by 8% from medium to hard soil. Additionally, axial forces provide a 9% decrease for medium soil and a 4% reduction for hard soil in a 10-floor building frame resistance system. There is a reduction of 3% from soft to medium soil and a reduction of 12% on hard soil regarding axial force. Meantime, the axial forces are lesser for medium soil by 13% compared to soft soil and less by 6 % for hard soil. The displacement is decreased by 6% in a 5-floor building frame system on medium soil and 11% on hard soil. However, the displacement of a 10-floor building structure is reduced by 10% on medium soil and 22% on hard soil. Displacement in a five-floor shear wall structure is decreased by 6% and 18% on medium and hard soil. Also, displacement reduces by 20% and 30% on medium and hard soil, respectively.

Brazil and Antarctica: a long way to meet each other

The review examines a Latin American researcher monograph devoted to the problems of Brazil’s Antarctic policy. As the review demonstrates, in terms of the current moment, this study includes in as much detail as possible a comprehensive examination of the polar interests of the South American “tropical giant”, as well as an extensive archival sources database on this topic. The author gives some forecasts of possible ways of de-velopment of the Brazilian Antarctic policy.

Spectral decomposition formula and moments of symmetric square $L$-functions

We prove a spectral decomposition formula for averages of Zagier $L$-series in terms of moments of symmetric square $L$-functions associated to Maass and holomorphic cusp forms of levels $4$, $16$, $64$.

Design of a Flexible Bionic Ankle Prosthesis Based on Subject-specific Modeling of the Human Musculoskeletal System

A variety of prosthetic ankles have been successfully developed to reproduce the locomotor ability for lower limb amputees in daily lives. However, they have not been shown to sufficiently improve the natural gait mechanics commonly observed in comparison to the able-bodied, perhaps due to over-simplified designs of functional musculoskeletal structures in prostheses. In this study, a flexible bionic ankle prosthesis with joints covered by soft material inclusions is developed on the basis of the human musculoskeletal system. First, the healthy side ankle–foot bones of a below-knee amputee were reconstructed by CT imaging. Three types of polyurethane rubber material configurations were then designed to mimic the soft tissues around the human ankle, providing stability and flexibility. Finite element simulations were conducted to determine the proper design of the rubber materials, evaluate the ankle stiffness under different external conditions, and calculate the rotation axes of the ankle during walking. The results showed that the bionic ankle had variable stiffness properties and could adapt to various road surfaces. It also had rotation axes similar to that of the human ankle, thus restoring the function of the talocrural and subtalar joints. The inclination and deviation angles of the talocrural axis, 86.2° and 75.1°, respectively, as well as the angles of the subtalar axis, 40.1° and 29.9°, were consistent with the literature. Finally, dynamic characteristics were investigated by gait measurements on the same subject, and the flexible bionic ankle prosthesis demonstrated natural gait mechanics during walking in terms of ankle angles and moments.

Nonlinear analysis of Euler beams resting on a tensionless soil with arbitrary configurations

BackgroundThe nonlinear interaction between an elastic Euler beam and a tensionless soil foundation is studied. The exact analytical solutions of the nonlinear problem are rather complicated. The main difficulty is imposing compatibility conditions at lift-off points. These points are determined as a part of the solution, although being needed to get the solution itself. In the current work, semi-analytical solutions are derived using the Rayleigh–Ritz method. The principle of vanishing variation of potential energy is adopted. The solution is approximated using a set of suitable trial functions. Accurate high-order approximate analytical solutions are obtained using MAXIMA symbolic manipulator. Lift-off points are identified through an iterative procedure and compatibility conditions are satisfied automatically. The methodology is designed to accommodate arbitrary configurations for the load distribution and the beam properties.ResultsExact solutions are revised briefly to verify the semi-analytical solutions in terms of deflection, bending moment, and shear. Semi-analytical solutions for constant beam properties including various support conditions and load distributions are verified. Convergence of high-order semi-analytical solutions is illustrated for cases including one and two contact points. A parametric study is provided to illustrate the effect of soil stiffness on the contact length. The case of a finite beam with free ends is considered. The semi-analytical solutions for variable beam moment of inertia are provided and verified.ConclusionsHighly accurate semi-analytical solutions can be obtained for the problem considered using the Rayleigh–Ritz method along with a symbolic manipulator. Arbitrary load and support configurations can be modeled, and the locations of lift-off points are well predicted. The semi-analytical solutions are extremely valuable for cases of variable moment inertia since exact solutions are rather rare.

Numerical modeling and nonlinear analysis of semi-rigid jointed steel frames

This paper investigates the effect of semi-rigid connection, geometric nonlinearity and material nonlinearity in steel frame analysis. To study the independent and combined effects of different nonlinearities, elastic and inelastic analyses are carried out using general purpose finite element software SAP2000. Connections are modeled as rotational springs and frame as one dimensional beam element. Verification and application of the simplified numerical model developed in the present study is demonstrated by considering different examples and comparing the results of present study with those available in the published literature. Numerical alternatives, key features about modeling and necessary input parameters are discussed in detail. Rotational springs are characterized by linear, bilinear, multi-linear or nonlinear moment-rotation relationships of the connection. Results in terms of beam moment and nodal displacement are presented for both elastic and inelastic analyses. With the increase in connection flexibility, beam mid-span moments and displacements increase, but beam-end moments decrease. It is observed that the influence of connection nonlinearity dominates over material and geometric nonlinearities.

Surrogate model for a mechanical metamaterial undergoing microstructure instabilities and phase transformations

This paper addresses the modeling of periodic metamaterials with microstructure instabilities. Such instabilities are produced by bistable elastic mechanisms, i.e., snap-through deformation mechanisms, inducing phase transformations. Metamaterials with these features can be used for energy dissipation in elastic regimes between other applications.A new surrogate model of the bistable mechanism to replace High-Fidelity Finite Element simulations is developed in two sequential stages. In the first stage, a semi-analytical model of the bistable structural element is presented. Following an approach taken from the literature, the analysis of the bistable element is generalized to include load cases that had not been considered in the original study. These loading conditions naturally happen in functionally 2D and 3D metamaterials with complex microarchitectures. In a second stage, a frame element with linear kinematics and small deformations is described. The constitutive relations of the frame element, i.e., axial stress and moment in terms of axial strain and curvature, follow the same equations of the semi-analytical model derived in the first stage. A Variational Principle of Energetic Equivalence supplies the link between the semi-analytical model of the curved beam and the frame element. In this way, the response of this frame element, of only six degrees of freedom, reproduces the non-linear geometric behavior of the bistable element.The surrogate model is particularly efficient for simulating a large number of unit cells of the metamaterial and with the capacity to reproduce its behavior under general loading conditions. Thus, it is appropriate to assessing the metamaterial limit behavior, typically concerning phenomena such as energy dissipation and hysteresis under closed load cycles.

FEM analysis of wasted tire chip and sand as construction material for piles

The pile foundation can be easily damaged in the earthquake event and there is a need to reinforce the foundation to protect the superstructure. The aim of this study is to propose a material for pile foundation by using wasted tire chips mixed with sand (i.e. sand-tire mixture) and study its effectiveness in an earthquake incident. This idea is learned from many sand-tire mixtures investigations. Laboratory monotonic triaxial tests were conducted based on the pure Nevada sand and sand-tire mixture (i.e. volume of sand to volume of tire was 6:4 in this study) as the input parameters for the subsequent numerical simulation. The numerical simulation was based on a centrifuge experimental results, which was also validated in this study. The simulation results show that the proposed method has a good effectiveness for a pile foundation, since the reduction in terms of the bending moment acting on the pile foundation is significant. In addition, even in the earthquake incident, the pile foundation still has the lateral support contributed from the adjacent sand-tire mixture, which is able to protect the pile foundation from buckling and fractured. This pile foundation behavior is different from that supported by the pure sand (i.e. without sand-tire mixture), which has zero lateral support to the pile foundation in the earthquake incident. However, there is an optimal reinforced length for the sand-tire mixture, where the effectiveness becomes insignificant.

Quantum synchronization and entanglement of indirectly coupled mechanical oscillators in cavity optomechanics: A numerical study

It is often conjectured that quantum synchronisation and entanglement are two independent properties which two coupled quantum systems may not exhibit at the same time. However, as both these properties can be understood in terms of the second order moments of a set of conjugate quadratures, there may exist specific conditions for simultaneous existence of entanglement and quantum synchronization. Here we present a theoretical scheme to achieve the same between two mechanical oscillators, which are indirectly coupled with each other via a coupling between two cavities. We show that in the presence of the cavity-oscillator coupling, quadratically varying with their displacements, these oscillators can be synchronized in the quantum sense and entangled as well, at times much longer than the decay time-scale of the cavity modes. Precisely speaking, we show that in the presence of quadratic coupling, entanglement criterion and quantum synchronization measure are simultaneously satisfied in steady state. This behaviour can be observed for a range of quadratic coupling, temperature, and frequency difference of the two oscillators.

The lift force on deformable and freely moving bubbles in linear shear flows

This paper provides a comprehensive explanation for the lift force acting on a freely deformable bubble rising in a linear shear flow and examines how the lift force scales with the undisturbed shear rate in cases governed by different lift force mechanisms. Four distinct flow mechanisms are identified from previous studies, and the associated bubble-induced vorticity dynamics are outlined. We provide a theoretical framework to qualitatively explain the lift force acting on a bubble in terms of moments of the bubble-induced vorticity. We support our theoretical framework with three-dimensional multiphase direct numerical simulations to illustrate how the vorticity dynamics associated with the four mechanisms generate the lift force. These findings provide a comprehensive explanation for the behaviour of the lift force in a wide range of relevant governing parameters. Additionally, our simulation results show how differently the lift force scales with the shear rate, depending on the dominating lift force mechanism. These results indicate that the shear rate should, in general, be accounted for in highly viscous flows (low Galilei numbers) or at significant bubble deformations (moderate-to-high Eötvös numbers) when modelling the lift force coefficient.

Mean-field models of dynamics on networks via moment closure: An automated procedure.

In the study of dynamics on networks, moment closure is a commonly used method to obtain low-dimensional evolution equationsamenable to analysis. The variables in the evolution equationsare mean counts of subgraph states and are referred to as moments. Due to interaction between neighbors, each moment equationis a function of higher-order moments, such that an infinite hierarchy of equationsarises. Hence, the derivation requires truncation at a given order and an approximation of the highest-order moments in terms of lower-order ones, known as a closure formula. Recent systematic approximations have either restricted focus to closed moment equationsfor SIR epidemic spreading or to unclosed moment equationsfor arbitrary dynamics. In this paper, we develop a general procedure that automates both derivation and closure of arbitrary order moment equationsfor dynamics with nearest-neighbor interactions on undirected networks. Automation of the closure step was made possible by our generalized closure scheme, which systematically decomposes the largest subgraphs into their smaller components. We show that this decomposition is exact if these components form a tree, there is independence at distances beyond their graph diameter, and there is spatial homogeneity. Testing our method for SIS epidemic spreading on lattices and random networks confirms that biases are larger for networks with many short cycles in regimes with long-range dependence. A Mathematica package that automates the moment closure is available for download.

Synthesis, mesomorphic properties and DFT calculations of new coumarin Schiff base-ester liquid crystals

ABSTRACT In the present work, two series of Coumarin based Schiff base-esters mesogenic compounds have been synthesised. The first series (KSC-(6–18)) comprises of Schiff base of alkoxy 4-formylbenzoate and 7-alkoxy-3-aminocoumarin with symmetric variation of alkoxy chain at the both ends that have been designed and prepared. In the second series (KC-(6–18)), octyloxy chain on coumarin end was kept constant with variation at the other end. All new mesogens were characterised using various analytical techniques including FTIR, NMR, elemental and mass spectral analysis. The textures of the mesomorphic properties were investigated using polarising optical microscope (POM) and differential scanning calorimetry (DSC). In series (KSC-(6–18)), on varying the alkyl chain length at the both end of molecules systematically, an enantiotropic smectic A phase behaviour was observed for compounds with chain lengths (n = 6, 8, 10, 12). Compounds of the (KSC-(6–18)) series with (n = 14, 16, 18) were non-mesogenic. In the (KC-(6–18)) series with octyloxy chain at coumarin end, an enantiotropic smectic A mesophase was observed for all compounds (n = 6-18). The DFT calculations have been carried out and the theoretical study was discussed in terms of dipole moment, molecular electrostatic potentials, frontier molecular orbitals and geometrical structure along with aspect ratio.